To solve the Zener diode problem, first determine the value of the series resistor when the load is connected to a 15-volt supply. Calculate the total current in the series resistor using the minimum Zener current and the load current, which has 10 volts across it. After selecting the resistor, analyze its impact on currents with a 20-volt supply and in the absence of a load resistor. The Zener diode will adjust its current to maintain a stable output voltage of 10 volts. Finally, ensure that the power rating of the Zener diode is not exceeded during operation.